Menu Close

Prove-that-cos-pi-9-1-3-cos-2pi-9-1-3-cos-4pi-9-1-3-3-3-2-9-1-3-1-3-




Question Number 190659 by Shrinava last updated on 08/Apr/23
Prove that:  ((cos (π/9)))^(1/3)  − ((cos ((2π)/9)))^(1/3)  − ((cos ((4π)/9)))^(1/3)   = ((3 − (3/2) (9)^(1/3) ))^(1/3)
$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}} \\ $$$$=\:\sqrt[{\mathrm{3}}]{\mathrm{3}\:−\:\frac{\mathrm{3}}{\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{9}}}\: \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *